The Ferrari team, with whom Schumacher won a record five drivers' titles in a row between 2000 and 2004, have organised a silent march in support of their former driver to be held outside the University hospital, Grenoble.

The march is certain to be a sombre and poignant occasion although those present will hope the day will bring encouraging news on the German former racing driver, who is in a critical but stable condition.

No update was given on Schumacher's condition by the hospital or his management on Thursday, which indicated that there had been no change, although his family did make their first statement since the accident in which they insisted the most successful driver in F1 history would keep fighting.

"Following Michael's skiing accident, we would like to thank the people from all around the world who have expressed their sympathy and sent their best wishes for his recovery," the Schumacher family statement read.

"They are giving us great support. We all know he is a fighter and will not give up. Thank you." Schumacher's family have remained at his bedside since the weekend.

Fan place get-well souvenirs on the fence at the Michael Schumacher cart centre in Kerpen, Germany. Photograph: Marius Becker/DPA/Corbis

The 91-time grand prix winner, who suffered major brain trauma in the accident which occurred when skiing off-piste in the resort of Meribel last Sunday, remains in an artificially-induced coma. It is believed that his life was saved by his skiing helmet, which split on impact.

Schumacher was initially conscious before deteriorating into a critical condition. Rescuers were on hand within minutes of the accident and he was airlifted to hospital, where neurosurgeons have operated twice to remove blood clots on the brain and reduce swelling.

Doctors have said the impact caused numerous brain injuries including intracranial hematomas (multiple blood clots), bilateral lesions and bruising of the brain.

An initial operation carried out on Sunday to reduce swelling was followed by a second to remove the largest of a number of clots in his brain.

Jacqueline Hubert, the hospital's director general, said on Tuesday that his condition had started to improve.

Amateur footage, captured on December 29, 2013, of seven-time Formula One world champion Michael Schumacher being airlifted by helicopter from the site of his skiing accident on the Dent de Burgin near Méribel in the French Alps. Schumacher is in a critical condition after suffering a brain haemorrhage in the accident and has undergone two operations.